Least Common Multiple of 1692 and 1700

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1692 and 1700 the smallest integer that is 719100 that is divisible by both numbers.

Least Common Multiple (LCM) of 1692 and 1700 is 719100.

LCM(1692,1700) = 719100

LCM of 1692 and 1700

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1692 and 1700

LCM of 1692 and 1700 is 719100

Least common multiple can be found by multiplying the highest exponent prime factors of 1692 and 1700. First we will calculate the prime factors of 1692 and 1700.

Prime Factorization of 1692


2 1692
2 846
3 423
3 141
47 47
1

Prime factors of 1692 are 2, 3,47. Prime factorization of 1692 in exponential form is:

1692 = 22×32×471

Prime Factorization of 1700


2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 1700 are 2, 5,17. Prime factorization of 1700 in exponential form is:

1700 = 22×52×171

Now multiplying the highest exponent prime factors to calculate the LCM of 1692 and 1700.

LCM(1692,1700) = 22×32×52×171×471
LCM(1692,1700) = 719100

Factors of 1692

List of positive integer factors of 1692 that divides 1692 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 47, 94, 141, 188, 282, 423, 564, 846, 1692

Factors of 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700

Least Common Multiple of 1692 and 1700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1692 and 1700, than apply into the LCM equation.

GCF(1692,1700) = 4
LCM(1692,1700) = ( 1692 × 1700) / 4
LCM(1692,1700) = 2876400 / 4
LCM(1692,1700) = 719100

Properties of LCM 1692 and 1700

(i) The LCM of 1700 and 1692 is associative

LCM of 1692 and 1700 = LCM of 1700 and 1692

Related Least Common Multiples of 1692

Related Least Common Multiples of 1700

Frequently Asked Questions on LCM of 1692 and 1700

1. What is the LCM of 1692 and 1700?

Answer: LCM of 1692 and 1700 is 719100.

2. What are the Factors of 1692?

Answer: Factors of 1692 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 47, 94, 141, 188, 282, 423, 564, 846, 1692. There are 18 integers that are factors of 1692. The greatest factor of 1692 is 1692.

3. What are the Factors of 1700?

Answer: Factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700. There are 18 integers that are factors of 1700. The greatest factor of 1700 is 1700.

4. How to Find the LCM of 1692 and 1700?

Answer:

Least Common Multiple of 1692 and 1700 = 719100

Step 1: Find the prime factorization of 1692

1692 = 2 x 2 x 3 x 3 x 47

Step 2: Find the prime factorization of 1700

1700 = 2 x 2 x 5 x 5 x 17

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 719100 = 2 x 2 x 3 x 3 x 5 x 5 x 17 x 47

Step 4: Therefore, the least common multiple of 1692 and 1700 is 719100.